What exactly are the differences between semantic and lexical-semantic networks?
According to Wikipedia  and 
Semantic Networks
 ,By John F. Sowa
This is an updated version of an article in the Encyclopedia of Artificial Intelligence, Wiley, 1987, second edition, 1992. 


  A semantic network is used when one has knowledge that is best
  understood as a set of concepts that are related to one another.


From Wikipedia:


  Most semantic networks are cognitively based. They also consist of arcs and nodes which can be organized into a taxonomic hierarchy. Semantic networks contributed ideas of spreading activation, inheritance, and nodes as proto-objects.


An example of semantic network is WordNet. It groups English words into synsets. Some semantic relations between these synsets are meronymy, hyponymy, etc.

On the other hand, Lexical semantic: 


  ...explores whether the meaning of a lexical unit is established by looking at its neighborhood in the semantic net (words it occurs with in natural sentences), or whether the meaning is already locally contained in the lexical unit.